University of Washington paleontologist Ward (Rare Earth ) clearly sets forth the premise of his provocative book: "changing atmospheric oxygen levels over the last 600 million years have caused significant evolutionary change in animals." He argues that, for extended periods, there was less than half the amount of oxygen present today in the atmosphere, and a need to develop respiratory systems to deal effectively with ambient oxygen levels has been the dominant factor in creating species diversity, extinctions and basic animal body plans. Ward takes readers on a tour from the Cambrian through the Permian to the Jurassic, examining the dominant life forms in each period and arguing that oxygen availability, or lack thereof, is responsible for the evolution of endothermy, egg shells, live births and most of the major extinctions in Earth's history. He also claims that dinosaurs were successful for so long because they were able to make use of primitive air sacs (that became fine-tuned in modern birds), thus enabling them to outcompete all others in their oxygen-depleted environment. Ward's ideas deserve careful scrutiny and are likely to be discussed broadly, although his often awkward writing gets in the way of his message. Illus. (Oct. 11)